Problem: Which of the following numbers is a factor of 140? ${3,4,6,8,12}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $140$ by each of our answer choices. $140 \div 3 = 46\text{ R }2$ $140 \div 4 = 35$ $140 \div 6 = 23\text{ R }2$ $140 \div 8 = 17\text{ R }4$ $140 \div 12 = 11\text{ R }8$ The only answer choice that divides into $140$ with no remainder is $4$ $ 35$ $4$ $140$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $140$ $140 = 2\times2\times5\times7 4 = 2\times2$ Therefore the only factor of $140$ out of our choices is $4$. We can say that $140$ is divisible by $4$.